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 A182609 Number of conjugacy classes in GL(n,19). 17
 1, 18, 360, 6840, 130302, 2475720, 47045520, 893864520, 16983555840, 322687560618, 6131066120640, 116490256285320, 2213314916460120, 42052983412605480, 799006685733239040, 15181127028931412160, 288441413566677788022, 5480386857766875373560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..250 FORMULA G.f.: Product_{k>=1} (1-x^k)/(1-19*x^k). - Alois P. Heinz, Nov 03 2012 MAPLE with (numtheory): b:= proc(n) b(n):= add(phi(d)*19^(n/d), d=divisors(n))/n-1 end: a:= proc(n) a(n):= `if`(n=0, 1,        add (add (d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)     end: seq (a(n), n=0..30);  # Alois P. Heinz, Nov 03 2012 MATHEMATICA b[n_] := Sum[EulerPhi[d]*19^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *) PROG (MAGMA) /* The program does not work for n>4: */ [1] cat [NumberOfClasses(GL(n, 19)) : n in [1..4]]; (PARI) N=66; x='x+O('x^N); gf=prod(n=1, N, (1-x^n)/(1-19*x^n)  ); v=Vec(gf) /* Joerg Arndt, Jan 24 2013 */ CROSSREFS Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182610, A182611, A182612. Sequence in context: A143168 A127585 A230348 * A086502 A259459 A099276 Adjacent sequences:  A182606 A182607 A182608 * A182610 A182611 A182612 KEYWORD nonn AUTHOR Klaus Brockhaus, Nov 23 2010 EXTENSIONS More terms from Alois P. Heinz, Nov 03 2012 MAGMA code edited by Vincenzo Librandi, Jan 24 2013 STATUS approved

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